This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…
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48 results for “beta operator”
Magnitude of manifolds linked to Riesz energies and beta functions.
problem Magnitude invariant and its geometric significance.
method Relating magnitude invariant to Brylinski's beta function and pseudodifferential analysis.
result Precise relation between magnitude invariant and beta function for closed manifolds.
The study pinches the Ricci functional on solvmanifolds, identifying special metrics.
problem Analyzing the Ricci functional on solvmanifolds.
method Using properties of the beta operator and left-invariant metrics.
result Solvsolitons and almost-abelian Lie groups are global maxima of the Ricci pinching functional.
We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta-gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a hermitian manifold, where the B-field 2-form is imaginary and proportional to the canonical form associat…
Betting Against (Bad) Betaq-fin.PM
Proposes a new factor to improve BAB strategies by recognizing bad-beta assets.
problem Investors often misprice assets based on beta, ignoring bad-beta.
method Double-sorting on beta and bad-beta to create a new factor.
result The Betting Against Bad Beta factor improves BAB strategies.
New f-Betas for portfolio optimization using f-divergence risk measures.
problem Optimizing portfolio performance under varying market conditions.
method Derive f-Betas and Hellinger-Betas, using f-divergence risk measures.
result Demonstrated new Beta metrics provide better performance under stress.
Study examines time-varying betas and their volatility in bank interest income and expense margins.
problem Understanding the variability of bank betas and their impact on net interest margins.
method Used state-space methods to estimate time-varying betas and conditional volatility.
result Substantial variation in interest income and expense betas, leading to varying net interest margin coefficients.
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
The Reactive Beta Modelq-fin.RM
A new beta model reduces bias in market neutral strategies.
problem Bias in beta estimation for market neutral strategies.
method Derive a metric of correlation with leverage effect to identify market beta and volatility changes.
result Empirical test confirms the reactive beta model's ability to reduce bias.
Machine learning improves beta forecasts, enhancing equity valuation and portfolio performance.
problem Improving beta forecasts for better equity valuation and portfolio performance.
method Using machine learning on a large cross-section of US stocks with various firm characteristics.
result Machine learning improves out-of-sample performance of asymmetric beta measures.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …
Beta Diffusioncs.LG
Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
Combining smart beta strategies improves portfolio performance.
problem Enhancing risk-adjusted returns through smart beta strategies.
method Construction of a monthly reweighted portfolio with two independent smart beta strategies: a long-short beta-neutral strategy and a minimized volatility portfolio.
result Combined strategy achieved a Sharpe Ratio of 1.35 in live trading.
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
In this paper, the geometric meaning of (alpha,beta)-norms is made clear. On this basis, we introduce a new class of Finsler metrics called general (alpha,beta)-metrics, which are defined by a Riemannian metric and an 1-form. These metrics not only generalize original (alpha,beta)-metrics naturally, but also include so…
Study beta function for convex billiard maps, linking spectral invariants.
problem Understanding spectral invariants of convex billiard maps.
method Birkhoff normal form via constructive generating functions, explicit beta function formula.
result Linked spectral invariants to beta function for convex billiard maps.
Beta-SOD detects and corrects noisy object re-identification using cosine similarity and Beta mixtures.
problem Noisy object re-identification in image datasets.
method Reframed Re-ID as a similarity task, using Siamese networks and Beta mixture models.
result Superior performance in noisy conditions compared to state-of-the-art methods.
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move…
Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approachstat.ME
Bayesian Beta regression for proportions in high dimensions with theoretical guarantees.
problem Modeling bounded continuous responses in high-dimensional settings with theoretical guarantees.
method Proposes a Bayesian approach using a tempered posterior with Horseshoe prior for shrinkage and variable selection.
result Demonstrates improved estimation accuracy and model interpretability in high-dimensional scenarios.
NeuralBeta uses deep learning to estimate beta, outperforming traditional methods.
problem Limitations of traditional beta estimation methods in capturing dynamic beta behavior.
method Neural networks with a new output layer for interpretability.
result NeuralBeta outperforms benchmark methods in dynamic beta estimation.
We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how…
Study explores geometric structure and prior for beta-logistic distribution.
problem Understanding the geometric structure and prior distributions of the beta-logistic distribution.
method Exploring dual geometric structure and uncovering -parallel prior.
result The beta-logistic distribution admits an -parallel prior for any real number .
The paper applies Fisher-Rao geometry to beta distributions for moment analysis.
problem Comparing and analyzing moments of probability distributions.
method Derived geodesic equations and sectional curvature on beta distributions' parameter space. Used Fisher-Rao geometry to map canonical moments to beta distributions.
result Uniqueness of Riemannian centroid in beta distributions' parameter space.
The paper proves optimizability implies inequalities for sampling.
problem Optimizing functions via Gradient Flow and sampling from Gibbs measures.
method Gradient Flow and Lyapunov potentials to establish inequalities.
result Optimizability via Gradient Flow implies Poincaré and Log-Sobolev Inequalities.
This paper introduces generalized betas accounting for higher order co-moment effects.
problem Financial returns data often deviate from normal assumptions in terms of higher order moments and contain outliers.
method Introduces CAPI and PP framework to calculate generalized betas optimizing the CAPI objective.
result Generalized betas optimize the CAPI objective, accounting for higher order co-moment effects.
Unified framework for scale-invariant representation learning using MAPCA.
problem Learning invariant representations in data.
method Metric-Aware Principal Component Analysis (MAPCA) based on generalized eigenproblem.
result MAPCA provides a unified geometric language for various self-supervised learning objectives.
Generalized Beta Divergencestat.ML
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr…
The Brylinski beta function is extended for coaxial layers on submanifolds.
problem Extending the Brylinski beta function to coaxial layers on submanifolds.
method Analytic continuation and computation of residues for the function.
result The Brylinski beta function has an analytic continuation with simple poles.
A beta function for double layers is defined and analyzed.
problem Defining and analyzing a beta function for double layers.
method Holomorphic function definition and analytic continuation.
result Residues of the beta function are integrals of invariants.
We derive and approximate the conjugate prior of Dirichlet and beta distributions.
problem Intractability of conjugate prior for Dirichlet and beta distributions.
method Derive conjugate prior, define closed-form approximation, and provide algorithm.
result Closed-form approximation enables fully tractable Bayesian treatment.
Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more app…
A new beta-VAE based regression model accelerates oilfield optimization studies.
problem Computational expense of full-physics reservoir simulations.
method beta-VAE for interpretable latent space representation, probabilistic dense layers for uncertainty quantification.
result Interpretable latent representation and quantified uncertainty for optimization decisions.
Hierarchical mixtures of Unigram models for short text clustering: The role of Beta-Liouville priorsstat.ML
Paper introduces a new text clustering model using Beta-Liouville priors.
problem Clustering short text data.
method Develops a hierarchical mixture model with Beta-Liouville priors for short text clustering.
result The Beta-Liouville distribution offers a more flexible correlation structure for short text clustering.
Stellar Braidingmath.GT
We construct a one-dimensional deformation retract of the unordered k-point configuration space of a star S. This retract suggests an explicit set of free generators Beta_k for the corresponding braid group of the star B_k and shows that the natural map from B_k-1 to B_k sends Beta_k-1 to Beta_k injectively.
New approach to Generalized Beta family using SDEs.
problem Understanding the Generalized Beta family of distributions.
method Using a mean-reverting SDE for a power of the variable, leading to a modified GB distribution.
result Provides alternative forms and cumulative distribution functions for GB distributions.
BS-VAE separates decoder variance and beta to improve VAE performance.
problem Blurriness in VAE outputs and difficulty in analyzing model performance.
method Explicitly separates beta and decoder variance in Beta-Sigma VAE.
result Superior performance in natural image synthesis and controllable parameters.
Robust Estimation of Realized Correlation: New Insight about Intraday Fluctuations in Market Betasecon.EM
New estimator reveals intraday betas mainly driven by correlations.
problem Intraday fluctuations in market betas due to time-varying volatility.
method Proposes a novel subsampled quadrant estimator for high-frequency financial data.
result Intraday variation in betas primarily driven by intraday variation in correlations.
In the present paper we study locally semiflat (we also call them semiintegrable) almost Grassmann structures. We establish necessary and sufficient conditions for an almost Grassmann structure to be alpha- or beta-semiintegrable. These conditions are expressed in terms of the fundamental tensors of almost Grassmann st…
The paper proves a unique solution to a shrinking flow equation converging to a soliton.
problem Existence and uniqueness of solutions to a specific shrinking flow equation.
method Anisotropic shrinking flow with speed based on support function and curvature radii.
result Smooth convergence to a soliton for certain parameter ranges.
Unified and noise-reduced data valuation framework for machine learning.
problem Quantifying the contribution of individual data points in machine learning.
method Beta Shapley, a generalization of Data Shapley, relaxes the efficiency axiom.
result Beta Shapley outperforms state-of-the-art data valuation methods on various ML tasks.
Study examines Blomqvist's beta and four concordance measures on copulas.
problem Relating Blomqvist's beta to other concordance measures.
method Estimating concordance measures on copulas with fixed beta.
result Novel method for estimating concordance measures.
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
This work extends alpha-beta divergences to complex data and finds closed-form solutions.
problem Approximating complex random vectors.
method Extending alpha-beta divergences to complex data and optimizing the alpha-beta mean distortion.
result Closed-form expression for the centroid of complex random vectors.
The study explains how market-makers' hedging affects stock volatility during gamma-squeeze events.
problem Endogenous volatility amplification in option markets during gamma-squeeze events.
method Developed a theoretical framework linking hedging behavior and market turbulence, incorporating beta-normalized volatility.
result Low-beta stocks amplify volatility more during gamma-squeeze events.
Bivariate Beta-LSTMcs.LG
Proposes a new LSTM gate structure using bivariate Beta distribution.
problem Inflexibility of sigmoid gates in modeling multi-modality and skewness, and lack of modeling correlation between gates.
method Introduces a bivariate Beta distribution gate structure within LSTM cells.
result Empirically shows higher gradient values and improved model performance.
Paper tests if beta coefficients in AMF model are consistent over time.
problem Testing time-invariance of beta coefficients in AMF model.
method Used AMF model with GIBS algorithm to identify relevant factors, compared to FF5 model.
result AMF model shows time-invariant beta coefficients for most periods, FF5 does not.
Proposes GPCA module for channel attention in CNNs using Gaussian processes.
problem Improving performance in visual tasks through effective channel selection.
method Integrates Gaussian processes into channel attention mechanisms for probabilistic modeling of channel correlations.
result Demonstrates improved performance of GPCA module in end-to-end CNN training.